Suppose that you run a grain farm that produces six types of grain at prices of $200, $250, $300, $375, $450, $500 per ton.
(a) If x = (x1, . . . , x6) is the commodity bundle vector (meaning that xi is the number of tons of grain i to be purchased), express the total cost of the commodity bundle as a dot product of two vectors in R6.
(b) A customer has a budget of $100,000 to be used to purchase your grain. Express the set of possible commodity bundle vectors that the customer can afford. Also describe the relevant budget hyperplane in R6.
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